Exponential space computation of Gröbner bases
Klaus Kühnle, Ernst W Mayr · 1996
Given a polynomial ideal and a term order, there is a unique reduced Gröbner basis and, for each polynomial, a unique normal form, namely the smallest (w.r.t. the term order) polynomial in the same coset. We consider the problem of finding this normal form for any given polynomial, without prior computation of the Gröbner basis. This is done by transforming a representation of the normal form into a system of linear equations and solving this system. Using the ability to find normal forms, we show how to obtain the Grobner basis in exponential space.